Or upgrade Lightroom to v6.8.
I recently set my Nikon D750 up with Windows-10 and LrCC2015.8 for a wedding photo-booth with laptop.
The camera stayed tethered for six hours, and even (automatically) resumed the connection when I changed the camera battery (surprised me!)
But sorry- little other advice to help.
Check that cable plugs are firmly connected, use a quality USB cable (not too long), check that computer 'power' options are not interfering (like screen-saver). Check that the computer destination for the photos is fully read/write permissions (I believe Canon writes to both camera card and computer).
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